Question

What is the third step when factoring the trinomial ax^2 + bx + c, after you have factored out a common factor in each term?

A.) Add the linear terms together.

B.) Multiply the factors together to check.

C.) Factor the simplifed trinomial.

D.) Distribute the common factor.

Answer 1

The trinomial is ax² + bx + c.

Step 1 : Find two numbers, m and n, with the product (m · n) of a · c or ac and the sum (ma + n) or (m + na) of b.

ax² + max + nx + mn

Step 2 : Factor the GCF from each grouping.

ax(x + m) + n(x + m)

Step 3 : Distribute the common factor : ab + ac = a(b + c).

(ax + n)(x + m).

The option D is correct.